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Visualization of multivariate data sets is often done by mapping data onto a low-dimensional display with nonlinear dimensionality reduction (NLDR) methods. Many NLDR methods are designed for tasks like manifold learning rather than low-dimensional visualization, and can perform poorly in visualization. We have introduced a formalism where NLDR for visualization is treated as an information retrieval task, and a novel NLDR method called the Neighbor Retrieval Visualizer (NeRV) which outperforms previous methods. The remaining concern is that NeRV has quadratic computational complexity with respect to the number of data. We introduce an efficient learning algorithm for NeRV where relationships between data are approximated through mixture modeling, yielding efficient computation with near-linear computational complexity with respect to the number of data. The method inherits the information retrieval interpretation from the original NeRV, it is much faster to optimize as the number of data grows, and it maintains good visualization performance.